Method and apparatus for determining the thickness of several layers superimposed on a substrate

Abstract

A method and apparatus for determining the thickness of at least one layer superimposed on a substrate, at least one of the layers or the substrate being a conductor of electricity. The method includes the steps of generating an electromagnetic alternating field in the vicinity of the outer most layer with a coil in order to cause any currents to be generated in the conductor which act upon the alternating field. The frequency of the alternating field is adjusted to at least two different frequencies and is measured at these frequencies. The thickness of the layers is then determined based on the measurements and the electromagnetic properties of the substrate and the layers.

We claim: 
     
       1. A method for determining the thickness of at least one layer on a substrate, at least one of said layers or said substrate being a conductor of electricity, comprising the steps of: (a) generating a primary electromagnetic alternating field with a coil in the immediate vicinity of an outermost layer, whereby eddy currents are generated in said conductor which generate a secondary electromagnetic alternating field;   (b) adjusting said primary alternating field to at least two different frequencies;   (c) measuring the combined primary and second alternating fields at said frequencies to determine the influence of said eddy current; and   (d) calculating the thickness of said layers in a model using said measurement and at least some electromagnetic properties of said substrate and said layers, where no electrical properties are pre-set in said model while free model parameters such as thickness and permeability are altered until said model reconstructs the measured response.   
     
     
       2. The method of claim 1 wherein step (d) further comprises: (d1) generating a first mathematic model describing said coil;   (d2) generating a second mathematic model describing said substrate and said layers and their influence upon said combined alternating field; and   (d3) introducing fixed values for at least some of the electromagnetic properties of the substrate and layers into said second model.   
     
     
       3. The method of claim 2 wherein a mathematic inversion model is used for said second mathematic model and further comprising the steps of: (e) introducing a presumed thickness into said mathematic inversion model on said calculation of said layer thickness;   (f) calculating said alternating field through said first model and said mathematic inversion model;   (g) comparing said calculated alternating field with the measurement of said alternating field;   (h) introducing a new value for said thickness into said mathematic inversion model; and   (i) repeating steps (f)-(g) until substantial correspondence is obtained between said calculated and said measured alternating fields.   
     
     
       4. The method of claim 1 wherein said electromagnetic properties include at least one of the dielectric constant, the electric conductivity, and the magnetic permeability of said substrate and layers. 
     
     
       5. The method of claim 1 wherein said measurement of the alternating field is done at various frequencies in order to calculate the layer thickness and electromagnetic properties that are unknown. 
     
     
       6. The method of claim 1 wherein step (c) is done over a range of frequencies extending over at least one order of magnitude. 
     
     
       7. The method of claim 6 wherein said frequency range includes at least 500 KHz-10 MHz. 
     
     
       8. The method of claim 1 wherein step (c) further comprises the steps of: placing a receiver coil close to the outer most layer;   measuring the impedance of said receiver coil; and   measuring the phase difference of a voltage across said receiver coil with respect to a current through said coil.   
     
     
       9. The method of claim 8 wherein said receiver coil and said coil are one coil. 
     
     
       10. The method of claim 8 further comprising the steps of: measuring the intensity of the current through said coil; and   measuring the amplitude and the phase position of the voltage across said receiver coil with respect to said current.   
     
     
       11. The method of claim 1 wherein said layer is a metal oxide, said substrate is a metal alloy forming a wall of a fuel rod in a nuclear reactor. 
     
     
       12. The method of claim 11 wherein a partially magnetic layer is on top of said metal oxide and the magnetic permeability of said partially magnetic layer is accounted for in said calculation. 
     
     
       13. The method of claim 11 wherein said substrate is a zirconium alloy and said metal oxide is zirconium dioxide. 
     
     
       14. An apparatus for determining the thickness of at least one layer on a substrate, at least one of said layers being a conductor of electricity, comprising: first means for generating an electromagnetic alternating field;   second means for measuring said field;   third means, communicating with said first means, for adjusting the frequency of said electromagnetic alternating field to at least two frequencies; and   fourth means, communicating with said second means, for calculating the thickness of said layer in a model using said measurement and at least some of the electromagnetic properties of said substrate and said layers, where no electrical properties are pre-set in said model while free model parameters such as thickness and permeability are altered until said model reconstructs the measured response.   
     
     
       15. The apparatus of claim 14 wherein said first means comprises a coil which is described by said mathematic model and said fourth means is adapted to use said model in its calculating. 
     
     
       16. The apparatus of claim 15 wherein said coil has a single layer of turns. 
     
     
       17. The apparatus of claim 15 wherein said mathematic model describes said coil as an equivalent coil having one turn. 
     
     
       18. The apparatus of claim 15 wherein said mathematic model describes said coil as at least two equivalent coils, a transmitter coil and a receiver coil. 
     
     
       19. The apparatus of claim 15 wherein said mathematical model comprises a first mathematical model describing said coil and a second mathematical model describing the constitution of said layers and said substrate and their influence on said alternating field, said fourth means further comprising means for introducing fixed values for at least some of the electromagnetic properties of said substrate and said layers into said second mathematic model. 
     
     
       20. The apparatus of claim 19 wherein said second model is a mathematic inversion model, said fourth means further comprising means for introducing a presumed thickness for said layer into said mathematic inversion model and means for comparing the result of the calculation with the measurement, whereby said comparison is repeated until a substantial correspondence is obtained between said calculated and measured alternating fields. 
     
     
       21. The apparatus of claim 14 wherein said second means comprises: at least a receiver coil arranged close to the outer most layer;   means for measuring the impedance of said receiver coil; and   means for measuring the phase difference of a voltage across said receiver coil with respect to a current flowing through a generating coil.   
     
     
       22. The apparatus of claim 21 wherein one coil is used as the receiving and generating coil. 
     
     
       23. The apparatus of claim 21 wherein said second means measures the amplitude and phase position of the voltage over said receiver coil with respect to the current through the generating coil, said second means including a means for comparing said voltage amplitude and the intensity of said current through the receiver coil. 
     
     
       24. The apparatus of claim 20 wherein said fourth means is adapted to use a mathematic inversion model to calculate the inductance of a coil.